Question

F(x)=x^2+3x-5. find and simplify f(x+h)-f(x)

Answer 1

`f(x + h) - f(x) = h^2 + 3h - 5`

Explanation:

Given

`f(x) = x^2 + 3x - 5`

Required

Find f(x + h) - f(x)

In functions:

`f(x + h) = f(x) + f(h)`

So:

`f(x + h) - f(x) = f(x) + f(h) - f(x)`

Collect Like Terms

`f(x + h) - f(x) = f(x) - f(x)+ f(h)`

`f(x + h) - f(x) = f(h)`

Solving for f(h)

`f(h) = h^2 + 3h - 5`

So:

`f(x + h) - f(x) = h^2 + 3h - 5`